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Plutarch's Boxes

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

All-variables Sudoku

The challenge is to find the values of the variables if you are to solve this Sudoku.


Age 11 to 14
Challenge Level


A bag contains 12 marbles.

There are more red than green but taking the green and blue together exceeds the number of reds.

The total number of yellow and green marbles is more than the total number of red and blue.

Find exactly how many of each colour there are in the bag.

How many different solutions can you find?